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Crystal field simulation by full configuration interaction
Journal of Luminescence 46 (1990) 375—379 North-Holland
375
CRYSTAL FIELD SIMULATION BY FULL CONFIGURATION INTFRACHON M. FAUCHER and D. GARCIA UFR 60210, CNRS, 1 FL A-Brian4 92195 Meudon-Céde~France Received 8 January 1990 Accepted 27 March 1990
3 ground configuration of neodymium in solids are simulated by a full 4f32p6/4f42p5 The crystal interaction field splittings of the 4f configuration calculation in the case of a two ion system. Realistic “intrinsic parameters” (such as those of Nd 203) can only be obtained by increasing the oxygen nuclear charge. The energy level scheme is compared with the one resulting from a one-electron model analysis.
1. Introduction The calculation of accurate ab-initio parameters istheory. still the stumbling block crystal field For main rare earth ions, the mainof work in the field was accomplished twenty years ago by Newman and coworkers [1—4].More recently [5,6] owing to modern computation techniques, an investigation was completed of all the possible mechanisms, up to second order in perturbation theory, which contribute to the crystal field and to the correlation crystal field. The calculations were applied to the Pr3~—Cl system. In particular, 4f, 2s 4f, 4d 4f, 2p 5d, 2s 5d, 4d 5d and 4f ni excitations together with a number of other processes were considered. The crystal problem was replaced by a two-ion model since crystal field effects of ligands in a cluster can be superimposed within a good approximation [7]. When compared to experimental values, the total calculated intrinsic crystal field parameter A 2 is too large, while A4 displays a good agreement and A6 is nearly two times too small. The authors point out that the shielding of A2 could be taken correctly into account by including third order diagrams in the calculation. Besides, they discovered a possible “source” of sixth order parameters, i.e. 4f nf excitations, In the present work, instead of utilizing a perturbation method, we perform, in a two-ion sys—~
—
—~
—
—+
—~
0022-2313/90/$03.50 © 1990
—
tern, a full configuration interaction calculation. The effect of the environment on the rare earth ion is restricted the interaction between rare 3~)4fto orbitals and the ligandthe (02_) earth (Nd valence 2p electrons. The two configurations which interact are 4f 32p6 and 4f42p5. The calculated energy levels are fitted by a one-electron model as if it was an experimental spectrum and the main features are discussed.
2. Crystal field calculation
—,
The characteristics of the computer program ATOME are described in ref. [8]. The matrix elements are evaluated on the basis of Slater determinantal functions, which eliminate the need for reduced matrix eletnents of the various operators for spectroscopic terms. The advantages of the method are: (a) a straightforward substitution of one rare earth for another can be made when desired, and (b) great simplicity for testing one- or two-electron formulas. For the free-ion part of the calculation, i.e. spin—orbit and two- and three-electron interactions, we utilise the previously fitted experimental parameters: Slater integrals, spin—orbit coupling constant, Tree’s a, ~8, ‘y parameters and Judd’s Tk parameters. For the crystal field effects, one- and
Elsevier Science Publishers B.V. (North-Holland)
376
M Faucher et al.
/
Crystalfield simulation byfull configuration interaction
two-electron integrals are explicitly introduced in the matrix elements. The configuration energy levels come directly out of the calculation. The electrons which do not belong to the f and p valence shells of the two ions are supposed to be frozen at the nuclei. The nonspherical contributions to the two-ion system energy are: the kinetic energy integrals: <1 I ~2/2 I the nuclear integrals:
be built up from individual ligands at coordinates R~,9~,q~,by the expression:
the Coulombic, hybridization and exchange integrals:
The power law exponent for k = 2 is uncertain since the second order parameters include important electrostatic contributions. The R 0(k) are fitted to give the best agreement between expression (1) and experimental B values. Expression in turn, gives the intrinsic parameters at any(2) distance. The procedure is applied to Nd 203 and NdAlO3, which are at the opposite ends of the nephelauxetic scale [14,15]. For each compound the intrinsic parameters created by an oxygen ligand at 2.3 A are calculated. The results are listed in table 1. The A2 values are deduced by the same power law as A4 and A6 and are therefore approximate. The two sets of intrinsic 3~inparameters crystals. delimit a reasonable range for Nd
— —
—
—
K! IQiig/’IP)
account for the following reason: from the oneelectron ionization energies of neodymium and 42s1 configuraoxygen [9],one can infer that the 4f tion is more than 200000 cm’ above 4f32s2. Thus the influence of 2s electrons of the ligand is mainly electrostatic via the integrals, and is therefore quite “point-charge”-like. The Nd—O distance is chosen to be 2.3 A which is a usual rare-earth/oxygen first neighbour distance in crystals. The wave functions basis sets for neodymium and oxygen are normalized (Schmidt procedure) combinations of Slater type orbitals [10,11]. Two-center, two-electron integrals are evaluated by the means of imbricated 32 point gauss quadratures. The probable errors are estimated by cornparing them to (a) the results of direct step by step calculations with decreasing interval sizes, and (b) to literature values [12]. In terms of energy, the maximum error is estimated as 5 cm’ for the largest Coulombic and hybridization integrals. Once the spherical is subtracted, the Coulombic integralscomponent range between 18 and 3140 cm’ and the 1. hybridization integrals between 10 The largest exchange integral and 2955tocm amounts 167 cm1 which is one order of magnitude smaller. 3. Intrinsic crystal field parameters
B
c(e~.9)~).
~Ak(RJ)
(1)
For one axial ligand, B~reduces to the intrinsic cfp Ak. In ref. [13] Newman proposes for rare earths with oxygen ligands the approximate power law: 11 for k = 4 and 6. (2) Ak(R) =Ak(Ro)(Ro/R)
Table 1 Rare earth and oxygen nuclear charges, energy gap between configurations and equivalent one-electron crystal field parameters for the ground configuration (in units of cm1). Compound
A A4 1141 1281
A6
1745 2053 (+18%)
1000 1310 (+31%)
230 375 (+63%)
1570 (—10%) 1935 (+11%)
1056 (+6%) 1160 (+16%)
260 (+13%) 279 (+21%)
Nd203 NdA1O3 6/4f22p5 interaction: 4f’2p QRE Qng E 5 4.0 5.7 50000 4.5 5.7 50000 4.0
5.8
50000
4.0
5.7
40000
2 1489 926
546 1398
4f32p~/4f~2p5 interaction: QRE
The superposition model [13] states that the total crystal field parameters (cfp) of a cluster can
=
Q
115 6.0
5.7
E5 50000
2039
1361
595
M. Faucher et al.
/
Crystalfield simulation by full configuration interaction
4. Results Our concern is to reproduce a calculation mimicking as closely as possible an experimental case. This means, since only two ions are involved, a calculation yielding an energy level scheme consistent with realistic intrinsic parameters (see the values for Nd203 and NdAIO3 in table 1) when interpreted on a one-electron basis. 4.1. 4f2p6/4f22p5 interaction A first series of crystal field calculations was applied to Ce3~via the 4f12p6/4f22p5 configuration interaction. This case is not really of practical interest owing to the small number 1 configuration, butofit sublevels provides belonging to thebasis 4f for preliminary calculations. a manageable The total number of involved levels in both configurations amounts only to 560 (14 + 546). The nuclear charges should exactly balance the negative charges of the outer electrons involved in the calculation. There are four such electrons in cerium and four in the oxygen atom, the other electrons being frozen at the nuclei. Therefore, the nuclear charges should be equal to 4 for the rare earth and the oxygen, the unique adjustable parameter being the energy gap between the two involved configurations. In fact, in order to obtain a realistic calculation, we had to increase the oxygen nuclear charge up to 5.7 (resulting in a —0.3 overall charge on the oxygen ion). This can be justified since a free ion calculation of the mean nuclear charge seen by the oxygen 2p electron gives about 5.2. However, a similar calculation applied to the neodymium 4f electron yields a value close to 24, which is highly improbable! The one-electron values ionizationvalue en1 of as athe reasonable ergies [9] give 50000 cm for the energy gap between the barycenters of the two configurations. Owing to Kramers degeneracy, the ground configuration levels are doubly degenerate. Theare 7 12p6 spectrum energy levels the resulting 4f analyzed in of terms of one-particle crystal field parameters (cfp). The nuclear charges and energy gap are varied and the resulting cfp are listed in table 1.
377
If the rare earth nuclear charge is increased from 4 to 4.5, the second, fourth and sixth order parameters increase by 18, 31 and 63%, respectively. The sixth order parameters increase more rapidly than the second and fourth order ones. If the oxygen nuclear charge is increased from 5.7 to 5.8, the cfp change by —10, + 6, and 13%, respectively. Finally, if the energy gap is decreased from 2, B~, B~and B~increase by 50 000 40 000 cm respectively. While all these 11, 16 toand 21%, manipulations result in a selective increase of B it seems difficult, by varying charges and gap width, to obtain intrinsic parameters similar to those of NdAIO 3. 4.2. 4f32p6/ 4!42p5 interaction +
This calculation involves a total of 6370 levels, 364 for the ground level and 6006 for the excited one. This case is of practical interest since several experimental spectra of Nd3 in crystals, comprising a hundred or more observed lines, have so far been fitted. The resulting configuration will be referred to as “ATOME”. The nuclear charges are 6 and 5.7 for neodymium and oxygen, respectively. The 85 lowest levels of “ATOME” were fitted to a one-electron crystal field Hamiltonian [16] and the resulting parameters are reported in table 1. They are not too far from the intrinsic parameters of Nd 203. Table 2 reports (column 3), the relative deviation between “ATOME” and some parametrically simulated levels. We chose isolated levels which are experimentally observed in real compounds without ambiguity. Table 2 refers to the total splittingdeviations of the levels. In columns and experi5, the relative are also listed for4 two mental spectra of Nd 203 and NdAIO3, respectively. The two last lines in table 2 give the crystal field strengths and the overall mean deviations of theThe three spectra. quality of the one-electron parametrization. can be appreciated by the magnitude of the mean deviation. For “ATOME”, it amounts to 19 cm1 which is a mediocre performance, compared to the values (14 and 11 cm’) corresponding to the two +
378
M. Faucher et al.
/
Crystalfieldsimulation by full configuration interaction
Table 2 Deviations between “ATOME”, experimental energy levels, and parametrically calculated levels. Level
4F19/2 4F 312 2H(2) 912 11,,2 2~1) 2P 2F(2) 3,.2 5,,2 Mean deviation of the fitting procedure Crystal field strength
Energy (cm’)
(~E~— ~EAT)lOO/~EAT
0 11500 14800 15000 24000 25000 37000 39000
—9 11 19 —6 13 25 —15 —34
3 —6 —8 —65 —5 —3 —3 37
—3 —15 —5 —17 1 4
19 515
14 422
11 386
experimental spectra (even if we somehow have to lower it to take into account the high value of the crystal field strength). One of the reasons for this high value is that the “ATOME” spectrum is slightly squeezed on The the net top, result compared the experimental spectra. is thattowhen many high-lying levels are included in the fitting procedure, the best cfp are too small to adjust the ground levels. Exactly the opposite is true in the interpretation of the experimental spectrum of Nd203 [15] where the mean crystal field strengths of sets fitting the excited levels are 1) ground and 422 and cm1, respectively. 371The (or ground 413 cm 4~ are the less divergent levels in the three simulations. The opposite signs in column 3 on one hand, and columns 4 and 5 on the other, are explained by the top flattening of the ground configuration 4f32p6. Not only 19/2 but all the lowest levels in “ATOME” (up to 17000 cm1) are well fitted. It is noteworthy that the important experimental deviation of the 2H(2)ll/ 2 level is not apparent in “ATOME”. Some isolated high deviations (up to 60 cm’) occur at higher energies. Numerical errors are probably not responsible for these discrepancies but, rather, many-electron processes. It seems that the one-electron approximation breaks down at the approach of boundary regions between the two configurations. It is difficult to explain the
(~E — Nd 203
NdA1O3
— —
opposite signs of the deviations in “ATOME” on one hand, and in Nd203 and 4F 4F NdA1O3 on the other. This occurs for 3/2, 9/2, and mainly for 2F(2) 712. 3~ and In the 3 twoin compounds LaF3earth : Nd is surLiYF which the rare 4 : Ndby fluorine ligands, the 2F(2) rounded 5/2 and 2F(2) 7/2 levels are also strongly deviant (approximately 40%) as in the “ATOME” case. Unfortunately, these high-lying levels are seldom observed in oxides. ~,
—
5. Conclusion The crystal field action of a single ligand on a neodymium ion Nd3~is handled by a full calculation mixing the configurations 4f 32p6 and 4f42p5. The effect of the environment on the rare earth ion is restricted to the f—p interaction between the 3~)and the ligand (02_) valence rare earth (Nd electrons. The resulting energy levels are fitted by a oneelectron crystal field Hamiltonian in order to detect “abnormal” levels particularly sensitive to many-electron effects. A comparison is made with the same process applied to experimental spectra. The quality of the fitting is better for the latter which suggests that the many-electron processes
M. Faucher et of
/
Crystalfieldsimulation by full configuration interaction
are magnified in the present calculation. On the other hand, the usually highly deviant 2H(2)1112 level is well fitted which leaves the origin of the discrepancy unknown.
References [1] M.M. Ellis and DJ. Newman, J. Chem. Phys. 47 (1967) 1986. [2] S.S. Bishton, M.M. Ellis, DJ. Newman and J. Smith, J~ Chem. Phys. 47 (1967) 4133. [3] M.M. Ellis and DJ. Newman, J. Chem. Phys. 49 (1968) 4037. [4] M.M. Curtis and DJ. Newman, J. Chem. Phys. 52 (1970) 1340.
379
[5] B. Ng and DJ. Newman, J. Chem. Phys. 87 (1987) 7096. [6] B. Ng and DJ. Newman, J. Chem. Phys. 87 (1987) 7110. [71DJ. Newman, Adv. Phys. 20 (1971) 197. [8] D. Garcia and M. Faucher, J. Chem. Phys. 90(1989) 5280. [91D. Garcia and M. Faucher, J. Chem. Phys. 82(1985) 5554. [10] M. Synek and L. Corsiglia, J. Chem. Phys. 48 (1968) 3121. [11] E. Clementi, C.CJ. Roothaan and M. Yoshiinine, Phys. Rev. 127 (1962) 1618. [12]1. Yasui and A. Saika, J. Chem. Phys. 76 (1982) 468. [13] DJ. Newman, Aust. J. Phys. 31 (1978) 79. [14]E. Antic-Fidancev, M. Lemaitre-Blaise and P. Caro, New J. Chem. 11 (1987) 467. [151 P. Caro, J. Derouet, L. Beaury and E. SOUIié, J. Chem. Phys. 70 (1979) 2542. [16] P. Porcher, unpublished computer program REEL.
375
CRYSTAL FIELD SIMULATION BY FULL CONFIGURATION INTFRACHON M. FAUCHER and D. GARCIA UFR 60210, CNRS, 1 FL A-Brian4 92195 Meudon-Céde~France Received 8 January 1990 Accepted 27 March 1990
3 ground configuration of neodymium in solids are simulated by a full 4f32p6/4f42p5 The crystal interaction field splittings of the 4f configuration calculation in the case of a two ion system. Realistic “intrinsic parameters” (such as those of Nd 203) can only be obtained by increasing the oxygen nuclear charge. The energy level scheme is compared with the one resulting from a one-electron model analysis.
1. Introduction The calculation of accurate ab-initio parameters istheory. still the stumbling block crystal field For main rare earth ions, the mainof work in the field was accomplished twenty years ago by Newman and coworkers [1—4].More recently [5,6] owing to modern computation techniques, an investigation was completed of all the possible mechanisms, up to second order in perturbation theory, which contribute to the crystal field and to the correlation crystal field. The calculations were applied to the Pr3~—Cl system. In particular, 4f, 2s 4f, 4d 4f, 2p 5d, 2s 5d, 4d 5d and 4f ni excitations together with a number of other processes were considered. The crystal problem was replaced by a two-ion model since crystal field effects of ligands in a cluster can be superimposed within a good approximation [7]. When compared to experimental values, the total calculated intrinsic crystal field parameter A 2 is too large, while A4 displays a good agreement and A6 is nearly two times too small. The authors point out that the shielding of A2 could be taken correctly into account by including third order diagrams in the calculation. Besides, they discovered a possible “source” of sixth order parameters, i.e. 4f nf excitations, In the present work, instead of utilizing a perturbation method, we perform, in a two-ion sys—~
—
—~
—
—+
—~
0022-2313/90/$03.50 © 1990
—
tern, a full configuration interaction calculation. The effect of the environment on the rare earth ion is restricted the interaction between rare 3~)4fto orbitals and the ligandthe (02_) earth (Nd valence 2p electrons. The two configurations which interact are 4f 32p6 and 4f42p5. The calculated energy levels are fitted by a one-electron model as if it was an experimental spectrum and the main features are discussed.
2. Crystal field calculation
—,
The characteristics of the computer program ATOME are described in ref. [8]. The matrix elements are evaluated on the basis of Slater determinantal functions, which eliminate the need for reduced matrix eletnents of the various operators for spectroscopic terms. The advantages of the method are: (a) a straightforward substitution of one rare earth for another can be made when desired, and (b) great simplicity for testing one- or two-electron formulas. For the free-ion part of the calculation, i.e. spin—orbit and two- and three-electron interactions, we utilise the previously fitted experimental parameters: Slater integrals, spin—orbit coupling constant, Tree’s a, ~8, ‘y parameters and Judd’s Tk parameters. For the crystal field effects, one- and
Elsevier Science Publishers B.V. (North-Holland)
376
M Faucher et al.
/
Crystalfield simulation byfull configuration interaction
two-electron integrals are explicitly introduced in the matrix elements. The configuration energy levels come directly out of the calculation. The electrons which do not belong to the f and p valence shells of the two ions are supposed to be frozen at the nuclei. The nonspherical contributions to the two-ion system energy are: the kinetic energy integrals: <1 I ~2/2 I the nuclear integrals:
be built up from individual ligands at coordinates R~,9~,q~,by the expression:
the Coulombic, hybridization and exchange integrals:
The power law exponent for k = 2 is uncertain since the second order parameters include important electrostatic contributions. The R 0(k) are fitted to give the best agreement between expression (1) and experimental B values. Expression in turn, gives the intrinsic parameters at any(2) distance. The procedure is applied to Nd 203 and NdAlO3, which are at the opposite ends of the nephelauxetic scale [14,15]. For each compound the intrinsic parameters created by an oxygen ligand at 2.3 A are calculated. The results are listed in table 1. The A2 values are deduced by the same power law as A4 and A6 and are therefore approximate. The two sets of intrinsic 3~inparameters crystals. delimit a reasonable range for Nd
— —
—
—
K! IQiig/’IP)
account for the following reason: from the oneelectron ionization energies of neodymium and 42s1 configuraoxygen [9],one can infer that the 4f tion is more than 200000 cm’ above 4f32s2. Thus the influence of 2s electrons of the ligand is mainly electrostatic via the
B
c(e~.9)~).
~Ak(RJ)
(1)
For one axial ligand, B~reduces to the intrinsic cfp Ak. In ref. [13] Newman proposes for rare earths with oxygen ligands the approximate power law: 11 for k = 4 and 6. (2) Ak(R) =Ak(Ro)(Ro/R)
Table 1 Rare earth and oxygen nuclear charges, energy gap between configurations and equivalent one-electron crystal field parameters for the ground configuration (in units of cm1). Compound
A A4 1141 1281
A6
1745 2053 (+18%)
1000 1310 (+31%)
230 375 (+63%)
1570 (—10%) 1935 (+11%)
1056 (+6%) 1160 (+16%)
260 (+13%) 279 (+21%)
Nd203 NdA1O3 6/4f22p5 interaction: 4f’2p QRE Qng E 5 4.0 5.7 50000 4.5 5.7 50000 4.0
5.8
50000
4.0
5.7
40000
2 1489 926
546 1398
4f32p~/4f~2p5 interaction: QRE
The superposition model [13] states that the total crystal field parameters (cfp) of a cluster can
=
Q
115 6.0
5.7
E5 50000
2039
1361
595
M. Faucher et al.
/
Crystalfield simulation by full configuration interaction
4. Results Our concern is to reproduce a calculation mimicking as closely as possible an experimental case. This means, since only two ions are involved, a calculation yielding an energy level scheme consistent with realistic intrinsic parameters (see the values for Nd203 and NdAIO3 in table 1) when interpreted on a one-electron basis. 4.1. 4f2p6/4f22p5 interaction A first series of crystal field calculations was applied to Ce3~via the 4f12p6/4f22p5 configuration interaction. This case is not really of practical interest owing to the small number 1 configuration, butofit sublevels provides belonging to thebasis 4f for preliminary calculations. a manageable The total number of involved levels in both configurations amounts only to 560 (14 + 546). The nuclear charges should exactly balance the negative charges of the outer electrons involved in the calculation. There are four such electrons in cerium and four in the oxygen atom, the other electrons being frozen at the nuclei. Therefore, the nuclear charges should be equal to 4 for the rare earth and the oxygen, the unique adjustable parameter being the energy gap between the two involved configurations. In fact, in order to obtain a realistic calculation, we had to increase the oxygen nuclear charge up to 5.7 (resulting in a —0.3 overall charge on the oxygen ion). This can be justified since a free ion calculation of the mean nuclear charge seen by the oxygen 2p electron gives about 5.2. However, a similar calculation applied to the neodymium 4f electron yields a value close to 24, which is highly improbable! The one-electron values ionizationvalue en1 of as athe reasonable ergies [9] give 50000 cm for the energy gap between the barycenters of the two configurations. Owing to Kramers degeneracy, the ground configuration levels are doubly degenerate. Theare 7 12p6 spectrum energy levels the resulting 4f analyzed in of terms of one-particle crystal field parameters (cfp). The nuclear charges and energy gap are varied and the resulting cfp are listed in table 1.
377
If the rare earth nuclear charge is increased from 4 to 4.5, the second, fourth and sixth order parameters increase by 18, 31 and 63%, respectively. The sixth order parameters increase more rapidly than the second and fourth order ones. If the oxygen nuclear charge is increased from 5.7 to 5.8, the cfp change by —10, + 6, and 13%, respectively. Finally, if the energy gap is decreased from 2, B~, B~and B~increase by 50 000 40 000 cm respectively. While all these 11, 16 toand 21%, manipulations result in a selective increase of B it seems difficult, by varying charges and gap width, to obtain intrinsic parameters similar to those of NdAIO 3. 4.2. 4f32p6/ 4!42p5 interaction +
This calculation involves a total of 6370 levels, 364 for the ground level and 6006 for the excited one. This case is of practical interest since several experimental spectra of Nd3 in crystals, comprising a hundred or more observed lines, have so far been fitted. The resulting configuration will be referred to as “ATOME”. The nuclear charges are 6 and 5.7 for neodymium and oxygen, respectively. The 85 lowest levels of “ATOME” were fitted to a one-electron crystal field Hamiltonian [16] and the resulting parameters are reported in table 1. They are not too far from the intrinsic parameters of Nd 203. Table 2 reports (column 3), the relative deviation between “ATOME” and some parametrically simulated levels. We chose isolated levels which are experimentally observed in real compounds without ambiguity. Table 2 refers to the total splittingdeviations of the levels. In columns and experi5, the relative are also listed for4 two mental spectra of Nd 203 and NdAIO3, respectively. The two last lines in table 2 give the crystal field strengths and the overall mean deviations of theThe three spectra. quality of the one-electron parametrization. can be appreciated by the magnitude of the mean deviation. For “ATOME”, it amounts to 19 cm1 which is a mediocre performance, compared to the values (14 and 11 cm’) corresponding to the two +
378
M. Faucher et al.
/
Crystalfieldsimulation by full configuration interaction
Table 2 Deviations between “ATOME”, experimental energy levels, and parametrically calculated levels. Level
4F19/2 4F 312 2H(2) 912 11,,2 2~1) 2P 2F(2) 3,.2 5,,2 Mean deviation of the fitting procedure Crystal field strength
Energy (cm’)
(~E~— ~EAT)lOO/~EAT
0 11500 14800 15000 24000 25000 37000 39000
—9 11 19 —6 13 25 —15 —34
3 —6 —8 —65 —5 —3 —3 37
—3 —15 —5 —17 1 4
19 515
14 422
11 386
experimental spectra (even if we somehow have to lower it to take into account the high value of the crystal field strength). One of the reasons for this high value is that the “ATOME” spectrum is slightly squeezed on The the net top, result compared the experimental spectra. is thattowhen many high-lying levels are included in the fitting procedure, the best cfp are too small to adjust the ground levels. Exactly the opposite is true in the interpretation of the experimental spectrum of Nd203 [15] where the mean crystal field strengths of sets fitting the excited levels are 1) ground and 422 and cm1, respectively. 371The (or ground 413 cm 4~ are the less divergent levels in the three simulations. The opposite signs in column 3 on one hand, and columns 4 and 5 on the other, are explained by the top flattening of the ground configuration 4f32p6. Not only 19/2 but all the lowest levels in “ATOME” (up to 17000 cm1) are well fitted. It is noteworthy that the important experimental deviation of the 2H(2)ll/ 2 level is not apparent in “ATOME”. Some isolated high deviations (up to 60 cm’) occur at higher energies. Numerical errors are probably not responsible for these discrepancies but, rather, many-electron processes. It seems that the one-electron approximation breaks down at the approach of boundary regions between the two configurations. It is difficult to explain the
(~E — Nd 203
NdA1O3
— —
opposite signs of the deviations in “ATOME” on one hand, and in Nd203 and 4F 4F NdA1O3 on the other. This occurs for 3/2, 9/2, and mainly for 2F(2) 712. 3~ and In the 3 twoin compounds LaF3earth : Nd is surLiYF which the rare 4 : Ndby fluorine ligands, the 2F(2) rounded 5/2 and 2F(2) 7/2 levels are also strongly deviant (approximately 40%) as in the “ATOME” case. Unfortunately, these high-lying levels are seldom observed in oxides. ~,
—
5. Conclusion The crystal field action of a single ligand on a neodymium ion Nd3~is handled by a full calculation mixing the configurations 4f 32p6 and 4f42p5. The effect of the environment on the rare earth ion is restricted to the f—p interaction between the 3~)and the ligand (02_) valence rare earth (Nd electrons. The resulting energy levels are fitted by a oneelectron crystal field Hamiltonian in order to detect “abnormal” levels particularly sensitive to many-electron effects. A comparison is made with the same process applied to experimental spectra. The quality of the fitting is better for the latter which suggests that the many-electron processes
M. Faucher et of
/
Crystalfieldsimulation by full configuration interaction
are magnified in the present calculation. On the other hand, the usually highly deviant 2H(2)1112 level is well fitted which leaves the origin of the discrepancy unknown.
References [1] M.M. Ellis and DJ. Newman, J. Chem. Phys. 47 (1967) 1986. [2] S.S. Bishton, M.M. Ellis, DJ. Newman and J. Smith, J~ Chem. Phys. 47 (1967) 4133. [3] M.M. Ellis and DJ. Newman, J. Chem. Phys. 49 (1968) 4037. [4] M.M. Curtis and DJ. Newman, J. Chem. Phys. 52 (1970) 1340.
379
[5] B. Ng and DJ. Newman, J. Chem. Phys. 87 (1987) 7096. [6] B. Ng and DJ. Newman, J. Chem. Phys. 87 (1987) 7110. [71DJ. Newman, Adv. Phys. 20 (1971) 197. [8] D. Garcia and M. Faucher, J. Chem. Phys. 90(1989) 5280. [91D. Garcia and M. Faucher, J. Chem. Phys. 82(1985) 5554. [10] M. Synek and L. Corsiglia, J. Chem. Phys. 48 (1968) 3121. [11] E. Clementi, C.CJ. Roothaan and M. Yoshiinine, Phys. Rev. 127 (1962) 1618. [12]1. Yasui and A. Saika, J. Chem. Phys. 76 (1982) 468. [13] DJ. Newman, Aust. J. Phys. 31 (1978) 79. [14]E. Antic-Fidancev, M. Lemaitre-Blaise and P. Caro, New J. Chem. 11 (1987) 467. [151 P. Caro, J. Derouet, L. Beaury and E. SOUIié, J. Chem. Phys. 70 (1979) 2542. [16] P. Porcher, unpublished computer program REEL.